2.3. Ellipsoid fitting

Napari-stress implements several algorithms for ellipse fitting. They all have in common that they return a napari vectors layer which represents the three major axes of the fitted ellipsoid. Napari-stress provides some further functionality to project the input pointcloud onto the surface of the fitted ellipsoid.

import napari_stress
import napari
import numpy as np

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
/tmp/ipykernel_1928/3187874842.py in <module>
----> 1 import napari_stress
      2 import napari
      3 import numpy as np

ModuleNotFoundError: No module named 'napari_stress'

2.3.1. Napari-stress implementation

This is a least-squares approach at ellipse fitting.

from napari_stress import approximation

pointcloud = napari_stress.get_droplet_point_cloud()[0][0][:, 1:]
ellipsoid = approximation.least_squares_ellipsoid(pointcloud)

viewer = napari.Viewer(ndisplay=3)
viewer.add_points(pointcloud, size=0.5, face_color='orange')
viewer.add_vectors(ellipsoid, edge_width=1, edge_color='magenta')
napari.utils.nbscreenshot(viewer)

WARNING: DirectWrite: CreateFontFaceFromHDC() failed (Indicates an error in an input file such as a font file.) for QFontDef(Family="8514oem", pointsize=12, pixelsize=20, styleHint=5, weight=50, stretch=100, hintingPreference=0) LOGFONT("8514oem", lfWidth=0, lfHeight=-20) dpi=192

Assistant skips harvesting pyclesperanto as it's not installed.

To display, where the initial input points would fall on the surface of the fitted ellipse, use the expand_points_on_ellipse() function:

fitted_points = approximation.expand_points_on_ellipse(ellipsoid, pointcloud)
viewer.add_points(fitted_points, size=0.5, face_color='cyan')
napari.utils.nbscreenshot(viewer)

2.3.2. Vedo implementation

This function re-implements the respective function from the vedo library. It applies a PCA-algorithm to a pointcloud to retrieve the major and minor axises of an ellipsoid, that comprises a set fraction of points within its volumne. The inside_fraction parameter controls how many points of the pointcloud will be located within the volume of the determined ellipsoid.

viewer2 = napari.Viewer(ndisplay=3)
viewer2.add_points(pointcloud, size=0.5, face_color='orange')

<Points layer 'pointcloud' at 0x2aa82710040>

ellipsoid_vedo = napari_stress.fit_ellipsoid_to_pointcloud_vectors(pointcloud, inside_fraction=0.675)
fitted_points_vedo = approximation.expand_points_on_ellipse(ellipsoid_vedo, pointcloud)

viewer2.add_vectors(ellipsoid_vedo, edge_width=1, edge_color='magenta')
viewer2.add_points(fitted_points_vedo, size=0.5, face_color='cyan')
napari.utils.nbscreenshot(viewer2)

2.3.3. Fit quality quantification

Lastly, if you wanted to quantify the fit remainder (i.e., the distance between the input and the fitted points), you can do this with approximation.pairwise_point_distances():

residues = approximation.pairwise_point_distances(pointcloud, fitted_points)

You can calculate the length of these vectors using numpy:

lengths = np.linalg.norm(residues[:, 1], axis=1)

viewer.add_vectors(residues, edge_width=1, features = {'lengths': lengths}, edge_color = 'lengths', edge_colormap = 'twilight')
napari.utils.nbscreenshot(viewer)